Theorists love to be competitive, but often enough we find out that they don't have to be like that. The SEP article on infinitesimals, for example, notes at one point:

It is of interest to note that Leibnizian infinitesimals (differentials) are realized in nonstandard analysis, and nilsquare infinitesimals in smooth infinitesimal analysis (for both types of analysis see below). In fact it has been shown to be possible to combine the two approaches, so creating an analytic framework realizing both Leibniz’s and Nieuwentijdt’s conceptions of infinitesimal.

So go to the Kripke-Lewis dialectic, that between the theory of transworld identity and the theory of otherworldly counterparts. Must these be opposed to each other? A Google search indicates no:

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My question, then, absent an ability to read the first of those articles (the second is openly readable), is this: are there attempts to reconcile the factions in the Kripke-Lewis dialectic such that they (the attempts) involve dividing objects into two classes, one of whose members are such that they enter into a distinctive counterpart relation, the other of whose members are such that they enter into a distinctive transworld-identity relation? This would mean, I suppose, a sort of "modal dualism" (then "modal tetralism"(?)):

  • There is a kind of substantial object such that examples of the kind aren't transworld-identical to objects in other worlds, but they do have counterparts.
  • There is a kind of substantial object such that examples of the kind are transworld-identical to objects in other worlds, but they don't have counterparts.

(Then: there are substances without counterparts or transworld identifications, and substances with both, perhaps overlapping.) Finally:

  • There are beings, perhaps God alone, for which the pertinent modal distinction collapses due to metaphysical simplicity appending to those beings: for these beings, there is no difference between having counterparts and being transworld-identifiable.

But now I should quote from Varzi again; maybe he's already what I'm looking for (and it wouldn't be the first time that he was, so to speak!):

Thus, from a formal perspective,4 the first point of departure is inessential to the idea that our modal discourse should be explained in terms of counterparts. One may see CT and the standard account as two species of the same genus, corresponding to the limit cases where no things are identical with their other-worldly counterparts or all things are, respectively.

I will continue to read through Varzi's discourse, to see if he has my example there; in the meantime, does anyone know of any sources for my example? Modulo Descartes, I would be tempted to say that counterpart-theoretic substance is matter, while transworld-identifiable substance is mind, perhaps (since we can think ourselves into, and think over/through, other possible worlds, if you will...).

  • In neither case is there a genuine question of which theory is true and which is false. In both cases it is merely a matter of which formalism is more convenient and has the fewest problems. Commented Dec 11, 2023 at 17:49
  • @DavidGudeman I'm not sure that's how Varzi sees it. At one point he writes, "We want to say that the choice between trans-world identity and counterparthood is strictly metaphysical," but whether he's speaking in his own voice or to express some other's opinion, it's not clear to me. He does go on about modal realism a lot, for whatever that's worth here. Commented Dec 11, 2023 at 18:00
  • Yes, I didn't mean to imply that's what the people who argue about these things believe, but I can't make coherent sense of the idea that there is a fact of the matter to resolve here. It's like asking whether sets are really just one-place relations vs. whether relations are really just sets of tuples. There is no fact of the matter to resolve. Either formalism is equally just a formalism. Commented Dec 11, 2023 at 20:26


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